def test_vector(self, alpha: np.ndarray) -> None:
paulis = PauliMatrices(2)
H = paulis.dot_product(alpha)
dFs0 = []
for p in paulis:
_, dF = dexpm_exact(H, p)
dFs0.append(dF)
dFs0_np = np.array(dFs0)
_, dFs1 = dexpmv(H, paulis.get_numpy())
assert np.allclose(dFs0_np, dFs1)
class PauliGate(QubitGate, DifferentiableUnitary, LocallyOptimizableUnitary):
"""A gate representing an arbitrary rotation."""
def __init__(self, size: int) -> None:
"""Create a PauliGate acting on `size` qubits."""
if size <= 0:
raise ValueError('Expected positive integer, got %d' % size)
self.size = size
self.paulis = PauliMatrices(self.size)
self.num_params = len(self.paulis)
self.sigmav = (-1j / self.get_dim()) * self.paulis.get_numpy()
def get_unitary(self, params: Sequence[float] = []) -> UnitaryMatrix:
"""Returns the unitary for this gate, see Unitary for more info."""
self.check_parameters(params)
H = dot_product(params, self.sigmav)
eiH = sp.linalg.expm(H)
return UnitaryMatrix(eiH, check_arguments=False)
def get_grad(self, params: Sequence[float] = []) -> np.ndarray:
"""Returns the gradient for this gate, see Gate for more info."""
self.check_parameters(params)
H = dot_product(params, self.sigmav)
_, dU = dexpmv(H, self.sigmav)
return dU
def get_unitary_and_grad(
self,
params: Sequence[float] = [],
) -> tuple[UnitaryMatrix, np.ndarray]:
"""Returns the unitary and gradient, see Gate for more info."""
self.check_parameters(params)
H = dot_product(params, self.sigmav)
U, dU = dexpmv(H, self.sigmav)
return UnitaryMatrix(U, check_arguments=False), dU
def optimize(self, env_matrix: np.ndarray) -> list[float]:
"""Returns optimal parameters with respect to an environment matrix."""
self.check_env_matrix(env_matrix)
U, _, Vh = sp.linalg.svd(env_matrix)
return list(pauli_expansion(unitary_log_no_i(
Vh.conj().T @ U.conj().T)))